In damp and cool conditions, Jones, who bogeyed his first hole of the day to slip seven shots behind Kuchar at that point, fought back with a round of 66 to play his way to Augusta National and move to 41st in the world ranking.
It was the Scottsdale based New South Welshman's first victory on either the PGA or Web.Com Tours and continues Australia's recent domination of the PGA Tour with Jason Day having won the Accenture, John Senden winning in Tampa, Steve Bowditch the Valero Texas Open and now Jones.
"The win means everything to me right now because that's what we play for is to win, to get -- to have Augusta as a benefit -- not a benefit, whatever the word is, sorry, but a reward for that win is amazing, said Jones after his win. "And I can't wait to get there and get some practice rounds in and hopefully play well, and hopefully three Aussies can win three in a row.
"I've always believed that I had the golf game to do it. It's more just getting comfortable in those certain situations. And I worked hard with my coach in Australia. He comes over a lot and comes over a lot more now."
For Kuchar, who led by four heading into the final round, it was the second week in succession where he has let slip a great winning opportunity.
Sergio Garcia threw out signals for his chances at Augusta with an impressive third place finish.